2024 · Q53
Consider the following for the next three (03) items that follow: Let ABC be a triangle right-angled at B. Let P be the point on BC such that BP = PC. If AB = 10 cm, ∠BAP = 45° and ∠CAP = θ. Consider the following statements :
- IThe line segment AP divides the area of the triangle ABC into two equal parts
- IIThe perimeter of the triangle APC is more than 46 cm
- IIIThe area of the triangle APC is 50 square cm Which of the statements given above are correct?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AI and II only
- BII and III only
- CI and III only
- DI, II and III
Explanation
I: AP is a median (P bisects BC), so it halves the area — correct. II: perimeter of APC = 10√2 + 10 + 10√5 ≈ 46.5 > 46 — correct. III: area of APC = half of ABC = ½×(½×10×20) = 50 — correct. All three hold — option D.